Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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GENERALIZED NORMALITY IN RING EXTENSIONS INVOLVING AMALGAMATED ALGEBRAS

  • Kwon, Tae In (Department of Mathematics, Changwon National University) ;
  • Kim, Hwankoo (Division of Computer & Information Engineering, Hoseo University)
  • Received : 2018.09.08
  • Accepted : 2018.12.05
  • Published : 2018.12.30
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Abstract

In this paper, seminormality and t-closedness in ring extensions involving amalgamated algebras are studied. Let $R{\subseteq}T$ be a ring extension with ideals $I{\subseteq}J$, respectively such that J is contained in the conductor of R in T. Assume that T is integral over R. Then it is shown that ($R{\bowtie}I$, $T{\bowtie}J$) is a seminormal (resp., t-closed) pair if and only if (R, T) is a seminormal (resp., t-closed) pair.

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References

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